Homework

Solve a math question

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Prompt Freeform Answer the question in the image with step by step solution. Response Here's how to multiply and simplify the expressions: 1. (√x + 2√3)² This is a binomial squared, which expands as (a + b)² = a² + 2ab + b². In this case, a = √x and b = 2√3. a² = (√x)² = x 2ab = 2(√x)(2√3) = 4√3x b² = (2√3)² = 4 * 3 = 12 Therefore, (√x + 2√3)² = x + 4√3x + 12 2. (√x + √3)(√x - √3) This is a difference of squares, which factors as (a + b)(a - b) = a² - b². Here, a = √x and b = √3. a² = (√x)² = x b² = (√3)² = 3 Therefore, (√x + √3)(√x - √3) = x - 3 In summary: (√x + 2√3)² = x + 4√3x + 12 (√x + √3)(√x - √3) = x - 3

Model: gemini-1.5-flash-002 Temperature: 0.2 Max output tokens: 8192 TopK: 40.0 TopP: 0.95